Posts Tagged ‘hubble expansion’

Dark Matter is an unnecessary ad hoc fix

January 11, 2012


The singularity at the center of a black hole must be unique and have testable consequences.

Dark Matter is an unnecessary ad hoc fix to fill in the blanks in the Friedmann model under the FLRW metric. Galactic supermassive black-holes exist as true physical singularities according to the Kretschmann invariant and Schwartzchild’s analysis of his spacetime metric under GR. Therefore, as point masses, they must possess a hyperbolic (1/kr) gravitational field, NOT a field that falls off as 1/r2. Now, k = constant = 1m, S.I., for dimensional integrity. It is not true that GR cannot tolerate hyperbolic spacetime geometries. “The universe is hyperbolic.” said Albert Einstein in his classic paper of 1915. An hyperbolic field will give constant orbital acceleration to orbiting bodies as far from the center of a black-hole as we might like to measure. This means that bodies near the periphery of a galaxy should seem to move at constant velocity because rotational acceleration does not drop to near zero there as with a 1/r2 inverse square law, it becomes consant. This constant velocity distribution effect has actually been measured and has given rise to the notion of Dark Matter.

Gravitation does not fall nearest to zero between galaxies in a cluster either. So they too can bend light and affect redshifts in ways that mimic Dark Matter. The rotation of galaxies in clusters is also influenced by the black-holes that they contain with their 1/kr gravitational potential profiles. The not quite counterbalanced redshift effects in the Sunyaev-Zeldovich phenomenon are influenced by the hyperbolic galactic and galactic cluster gravitational fields that exist as light falls out of such clusters and super-clusters into a large void and as it climbs out of it again after the universe has expanded by another billion light years or more.

Scientists are mapping, not Dark Matter, but the huge extent of the network of hyperbolic galactic and super-galactic gravitational fields that behave like Dark Matter because of the mathematical properties of the hyperbolic gravitational field are similar to that expected for Dark Matter.

Primordial massive and supermassive black-holes with their 1/kr galactic gravitational fields can also mimic the “halos” of dark Matter that are postulated to have existed just after the big bang and before the emission of the cosmic microwave background. There is nothing that Dark Matter explains that cannot be accounted for just as well or better by the hyperbolic black hole gravitational field.

The hyperbolic 1/kr supermassive black-hole galactic gravitational field explains “the Dark Matter Effect” without Dark Matter and it is more parsimonious and is a falsifiable hypothesis, unlike Dark Matter which is revised every time no Dark Matter is found.

The conditions for validity of Birkhoff’s Theorem are not met for real black-holes. Therefore, Birkhoff’s Theorem does not apply. It sometimes may be used as a first approximation, but it cannot be depended upon as a rigid rule for precise calculations. “The physics near at the extreme curvature of a black-hole singularity is not well defined”. This covers Birkhoff’s too.

It does too matter how the internal mass is distributed if it is contained within a single point. Then, in fact, it is NOT distributed at all! This is the point of Kretschmann’s invariant and Schwartzschild’s GR analysis of the consequences of his metric. Ordinarily, the distribution would not matter. But, a singularity must be different. If this is not explicitly acknowledged in some way, then to say there is a singularity with such intense curvature of spacetime in its vicinity that the laws of physics must begin to break down is a meaningless fatuous gesture to humility. It is false humility if it has no ameliorating effect on professional arrogance. Please, do not just restate Birkhoff.

I contend there is a loophole here or a gross misinterpretation. The consensus interpretation of Birkhoff and of Schwartzschild/Kretschmann cannot both be true at the same time. There must be a measureable consequence of the presence of a singularity that is beyond imaginary untestable gedanken experiments. The test is the hyperbolic gravitational field. It results in a nonzero constant rotational velocity distribution effect in spiral galaxies, ellipticals, globulars and galactic clusters. This is easier to believe than Dark Matter.

The very same phenomena that are used to argue for Dark Matter can be used to argue for the hyperbolic field. So, it is testable. But, how do we choose between them? I think that Occam ’s razor is the principle of choice here. WIMPS and neutralinos and the other oddball particles that have been proposed require ad hoc additions to theories or their complete rewrites. The hyperbolic field is far simpler. All that is needed is acknowledgement that the black hole singularity is unique. No rewrite of GR. No undetectable new heavy particles that get given self-serving, revised, lower detection limits every time they are determined to be really undetectable.

There seems to be a tendency of cosmologists to think inside the box. They never really consider anything that is outside the consensus. So too do journal editors rely on  conventional wisdom. They would all have been supremely comfortable with the Pope’s decision to censor Galileo.

“Cosmologists are always wrong, but never in doubt.”   Lev Landau

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A potential energy diagram is perfectly possible for a hyperbolic black-hole gravitational field

January 11, 2012

The “normal” Newtonian potential energy diagram derived from the inverse square relation versus the hyperbolic black hole gravitational potential energy diagram derived from the inverse (1/kr) relation

First of all, note that a potential energy diagram is perfectly possible for a hyperbolic black-hole gravitational field. The only trouble is with convention. Normally, one takes potential energy U as U = 0 at r = infinity. But, U keeps increasing forever with increasing r in the case of the HBH field. It does not level off to an asymptotic value. So, we would need to adopt a different convention, with U = 0 at r = 1. Then, we would have to remember that all U computed for the HBH case will need to be multiplied by -1 in order to be consistent with conventional usage.

We could represent how the ultra-massive universe excited inflaton HBH gravitational field collapses or transitions to the conventional inverse square field, thereby donating its potential energy to what is increasingly an inverse square gravitational universe, accelerating its expansion in the latter 2/3 of its evolution. We might use weighting factors. We could use a linear weighting factor or maybe an inverse square exponential form or even an hyperbolic expression.

Using x = r in the above diagram, let us try weight for the inverse square derived contribution, S = % and weight for the hyperbolic contribution, H = 1.00 – S, 0.00 < S < 1.00, so that U = S( -1/r +1) + (1.00 – S)ln(r), then total U will transition smoothly from the HBH hyperbolic potential energy to the inverse square potential. Here, 1 is a translation amount to let the inverse square derived curve superpose upon the hyperbolicaly derived. The potential energy lost by the HBH phase of the universe is made up by a gain in kinetic energy of expansion in the inverse square phase.

Remember, it is legitimate to think of Hubble expansion of spacetime carrying the objects embedded within it as a kinematic growth process. One need not always regard it as a “stretching” of spacetime, though for some other purposes, this may help.

Obviously, the resulting composite curve will have a significant positive slope on the right, connoting Dark Energy. But, the curves explicitly describe Dark Matter. So there is a strong link between DM and DE.

There have been misstatements and misinterpretations of Birkhoff’s Theorem. For instance, it has been shown by Kristin Schleich and Donald M. Witt (“A simple proof of Birkhoff’s theorem for cosmological constant”, arXiv: 09084110v2, 27oc09) that Birkhoff does not demand staticity in spherically symmetric solutions to Einstein’s vacuum field equations. Static solutions have heretofore been thought of as being required. There may be other misstatements and misinterpretations that are not yet recognized.

For instance, Birkhoff’s Theorem must actually leave black hole singular gravitational fields as an exception to the commonly quoted rigid rule that only asymptotically flat (commonly assumed meaning: inverse square) gravitational fields are allowed. Otherwise there is no way to measure or unequivocally determine that the center of a black hole is a singularity since electric charge and gravity are the only items the influence of which can escape the interior of a black hole.  Then the theories of Schwarzschild and Kretschmann that say such singularities are physically real are largely meaningless as unfalsifiable hypotheses.

There simply must be a measurable consequence of a true singularity at the center of a black hole or else its existence cannot be postulated. That the mathematics seems so very precise is not good enough. There must be a way to experimentally verify or falsify the equations.

If the gravitational singularity at the center of a super-massive galactic black hole results in a hyperbolic gravitational field, there is a way. By measuring the velocity distribution of stars in the surrounding galactic disk, it can be determined if they move with a constant velocity, v = (GM)^½ at large r, as they must if they move in a hyperbolic gravitational field. As a matter of fact, the velocities of stars in spiral galaxies do indeed move with constant velocity at large r. This can be seen as proof of a singularity at the center of a spiral galaxy’s black hole.

We often state that “The laws of physics must break down at the incredibly tight curvature of spacetime near the singularity of a black hole”. What does this mean? One thing it could mean is that Birkhoff’s Theorem breaks down too. The metrics to which Birkhoff applies probably are not strictly valid near the singularities that they themselves predict so, the “asymptotically flat” dictum may not be strictly true either. Otherwise, our cautionary statement is meaningless.

Besides, the intense benefit brought by the postulate of a hyperbolic galactic super-massive black hole gravitational field is too great to be ignored. It explains the anomalous stellar velocity distributions in galaxies, anomalous velocity distributions in galactic clusters, galactic lensing phenomena, temperature distributions within galaxies, Bullet Cluster type apparent offsets in the barycenters of colliding galaxy clusters, etc. It does everything that Dark Matter is supposed to do! So, Dark Matter is an unnecessary complication that violates Occam’s Rule.

Cosmologists will not like this idea. The LCDM model would have to be drastically revised. The consensus would have to change. Since journal editors and referees endorse only papers that conform to the consensus (they would have been comfortable with the Pope’s decision to censor Galileo), no-one will publish a paper that challenges the commonly accepted interpretation of Birkhoff’s Theorem. And, if Birkhoff does break down in the vicinity of a gravitational singularity, how can it ever be proven? One would have to develop a whole new physics of the ultra strong curvature near black hole singularities. Unless it also had consequences outside the black hole, such a theory could not be falsified so, it could not be admitted as a part of science.

Catch 22 says “Anyone who wants to get out of combat duty isn’t really crazy.” Hence, pilots who request a mental fitness evaluation are sane, and therefore must fly in combat. We would be better off flying in combat duty than trying to fly the hyperbolic super-massive galactic gravitational field into some journal’s pages.

The amazing thing is that the HBHG field does have consequences outside the BH and the event horizon.

Origins, emergence and eschatology of the Universe: Dark Energy

December 14, 2011

Should we mean “the universe” or “the meta-verse” or “the multi-verse”? (Hugh Everett)

Presumably, when the universe formed from an ensemble of some sort of “inflaton” point particles (Alan Guth) as a statistically inevitable child of an extremely excited field, possibly the gravitational field itself, its hyperbolic (proportional to 1/r) field began to collapse into a parabolic (1/r^2) one. That collapse continues to this day. But, the process is almost done. There cannot be an infinite amount of energy sequestered in the hyperbolic 1/r field that would be available to fuel acceleration of the Hubble expansion rate by such a transformation. Transition to a lower potential energy parabolic field must provide a distinctly limited supply of extra impetus. Surely, after 13.72 billion years, the (1/r) potential energy mainspring has almost run down by now. The remaining (1/r) potential energy is called Dark Energy.

It accounts for the “missing mass ” in audits of universe contents and provides a convenient, theoretically rigorous and parsimonious basis for “acceleration”. Dark Energy could account for around 80% of the universe’s total mass, but audits are not so accurate. Still, The Mainspring still has enough oomph to last for at least another 140 billion years more!

The hyper-excited gravitational field sprang into existence simply because it could. It came to be in a tremendously excited state because very high excited states are much more probable than lower ones, because of the zero point cut-off. This is just like virtual particles come to exist and be annihilated all the time on the quantum level (this is confirmed by experiment). None of them become universes, though, because there is already one here. It’s a sort of a Pauli exclusion principle.

There has been some confusion. So, let us switch definitions of r. In the following, r is the rate of acceleration of expansion of the universe (or rotational acceleration around black-hole).

If the acceleration of the expansion rate is called a, and its present value is called P, then a = P at any given time, including the present. The simplest equation for the expansion rate’s effect on P would be an exponential decay expression, P = hoe^(-rt), where ho is an initial value for h, r is the rate of increase in this expansion and t is time.

We can get an estimate of a value for ho from Alan Guth’s formulation of the theory of simple inflation. The present values of both the expansion rate, P1, and acceleration rate, r, is observable. We can set t = 1, for the present value of t. So, we can summarize all relevant observations with this simple equation or the associated exponential expansion equation, R = Roe^(rt),where R is the putative instantaneous “radius” or scale factor of the universe.

The current value of the expansion rate is Ho, the Hubble “constant”, so P1 = Ho.

Back to our original definition of r (not R) as a radius or scale factor:

Exponential decay equations exhibit what is called a “dormancy” period or final plateau region. In this part of the discussion, here, r refers to distance from a center of rotation. Sorry. I missed this inconsistency in previous posts. I need a nicer symbol for the exponential period, another name for r; maybe Cyrillic backward “R” ? May be lower case Cyrillic “r” ?

The hyperbolic 1/r curve levels off near zero and continues to subside gently almost linearly for an indefinite time. Plot a graph yourself on the back of an envelope! Use mass M = 1, the smaller mass drops out for acceleration. And, assume G is any self consistent constant like G = 1. This is just for comparison purposes, so it matters not. The equation for orbital acceleration around a galaxy, say, levels off to a constant, even at infinity, for a hyperbolic 1/r black-hole galactic gravitational field potential diagram. (You have just DERIVED modified Newtonian Dynamics or MOND!) You must multiply r by the constant k = 1m (Systeme Internationale) for dimensional purity.

The current state of the universe itself may be considered as being in this (1/r) exponential decay dormancy or plateau period. The conclusion here is that acceleration of expansion may continue for a long time while very slowly decreasing nearer to zero.

The black-hole rotational acceleration connection implies that the universe may be rotating very very slowly right now. But, we cannot know. We would have to observe the universe from the outside, from the perspective of the meta-universe, to tell. From the standpoint of general relativity, we simply cannot tell from our perspective her and now.

Yet, in other words, even with acknowledged acceleration of the Hubble expansion rate, there does not necessarily have to be a “Big Rip” wherein the fabric of the cosmos is irreparably torn apart as expansion proceeds beyond a certain point.

By the way, “M Theory” doesn’t exist. M Theory is just an “ideal”. Brane Theory is not M Theory. Neither has ever predicted anything that can be experimentally verified and neither is falsifiable. Therefore, they cannot qualify as legitimate scientific propositiions. Not one single unique result has ever come from either. Furthermore, they are both unnecessary. Shrewd development of general relativity and quantum are slowly causing both to merge. What’s the hurry? Let true “M Theory” and “Brane theory” grow organically out of quantum and GR. Each step will be independently validated, then. No worry.

Origins, emergence and eschatology are fertile fields for philosophers. This is why we scientists are sometimes called “Doctors of Philosophy”, Ph.D.    Doctorae Philosophi.    I took Latin for three years and I am still not sure of this. German and Russian too, but this is no help. What happened to my old Latin grammar texts?